The main points of this paper are :—
(i) The construction of a linear substitution from its poles or linear invariants and its multipliers (§§3, 7);
(ii) a formula for r repetitions of a substitution (§ 4);
(iii) a specification of the types of linear substitutions of order r, with examples of the simplest of those types(§§9ff.);
(iv) The geometrical illustration of the case of three variables (§§15 ff.)
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